FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2171513529> ?p ?o ?g. }

• W2171513529 abstract "1 . Introduction In a previous paper [2] the senior authors proved the following theorem: Let G, = GI (n ;cn 2 ) be a graph of n vertices and cn 2 edges, c a positive constant . Then for n sufficiently large there is always a subgraph G 2 = G2 (m ;f(c)n 2 ) of G, every two edges of which lie together on a cycle of length at most. 6 in G 2 , and if two edges of G 2 have a common vertex they are on a cycle of length 4 in G 2 . In that paper, we did not determine f(c) explicitly although the arguments used would yield something of the form f(c) _ 01c 3 . Here we replace c by n-e for e small and to some extent determine f(n ') . That is, we consider G 1 = G 21 (n ;n £ ) and try to find the subgraph G 2 having the largest number of edges with each pair of these edges on a short cycle . This problem leads to surprising and perhaps unexpected complications . Ode remark that in our previous paper we also discussed hypergraphs . In this paper, we do not do this but hope to return to that problem in the future (for the SENIOR author of course there may not be a future) . Here we prove the following theorem : For sufficiently large n each G 1 = G 1 (n ;n2-L ) contains a G 2 = G 2 (m ;cn2-3c ), where c does not depend on m, n, or c, in which every two edges are on a cycle of length at most 6 in G 2 , and that apart from the value of c this result is the best possible, i .e ., 3e cannot be replaced by any smaller value . If we further insist that any two edges of G 2 which have a common vertex are on a cycle of length 4 in G 2 then we can only show that there exists a G 2 = G 2 (m,cn 2-5c ), but here we do not know if 5c is best possible, and we cannot exclude the" @default.
• W2171513529 created "2016-06-24" @default.
• W2171513529 creator A5018877156 @default.
• W2171513529 creator A5035271865 @default.
• W2171513529 creator A5072612870 @default.
• W2171513529 date "1984-01-01" @default.
• W2171513529 modified "2023-10-16" @default.
• W2171513529 title "MORE RESULTS ON SUBGRAPHS WITH MANY SHORT CYCLES" @default.
• W2171513529 cites W1510730180 @default.
• W2171513529 cites W1552744309 @default.
• W2171513529 hasPublicationYear "1984" @default.
• W2171513529 type Work @default.
• W2171513529 sameAs 2171513529 @default.
• W2171513529 citedByCount "1" @default.
• W2171513529 crossrefType "journal-article" @default.
• W2171513529 hasAuthorship W2171513529A5018877156 @default.
• W2171513529 hasAuthorship W2171513529A5035271865 @default.
• W2171513529 hasAuthorship W2171513529A5072612870 @default.
• W2171513529 hasConcept C114614502 @default.
• W2171513529 hasConcept C132525143 @default.
• W2171513529 hasConcept C199360897 @default.
• W2171513529 hasConcept C2777027219 @default.
• W2171513529 hasConcept C2983226441 @default.
• W2171513529 hasConcept C33923547 @default.
• W2171513529 hasConcept C41008148 @default.
• W2171513529 hasConcept C80899671 @default.
• W2171513529 hasConceptScore W2171513529C114614502 @default.
• W2171513529 hasConceptScore W2171513529C132525143 @default.
• W2171513529 hasConceptScore W2171513529C199360897 @default.
• W2171513529 hasConceptScore W2171513529C2777027219 @default.
• W2171513529 hasConceptScore W2171513529C2983226441 @default.
• W2171513529 hasConceptScore W2171513529C33923547 @default.
• W2171513529 hasConceptScore W2171513529C41008148 @default.
• W2171513529 hasConceptScore W2171513529C80899671 @default.
• W2171513529 hasLocation W21715135291 @default.
• W2171513529 hasOpenAccess W2171513529 @default.
• W2171513529 hasPrimaryLocation W21715135291 @default.
• W2171513529 hasRelatedWork W1582204707 @default.
• W2171513529 hasRelatedWork W1676901480 @default.
• W2171513529 hasRelatedWork W1767752187 @default.
• W2171513529 hasRelatedWork W2031357976 @default.
• W2171513529 hasRelatedWork W2067297986 @default.
• W2171513529 hasRelatedWork W2165617531 @default.
• W2171513529 hasRelatedWork W2208548938 @default.
• W2171513529 hasRelatedWork W2293971275 @default.
• W2171513529 hasRelatedWork W2507224362 @default.
• W2171513529 hasRelatedWork W2768269438 @default.
• W2171513529 hasRelatedWork W2964741630 @default.
• W2171513529 hasRelatedWork W3009508895 @default.
• W2171513529 hasRelatedWork W3046002007 @default.
• W2171513529 hasRelatedWork W3104038630 @default.
• W2171513529 hasRelatedWork W3203316337 @default.
• W2171513529 hasRelatedWork W46182886 @default.
• W2171513529 hasRelatedWork W76207694 @default.
• W2171513529 hasRelatedWork W88846352 @default.
• W2171513529 hasRelatedWork W2119780280 @default.
• W2171513529 hasRelatedWork W2185692475 @default.
• W2171513529 isParatext "false" @default.
• W2171513529 isRetracted "false" @default.
• W2171513529 magId "2171513529" @default.
• W2171513529 workType "article" @default.